Mathematical modeling of the contour evolution of heavy plates in hot rolling

This paper deals with modeling of the contour evolution of heavy plates in hot rolling. During the rolling process asymmetric rolling conditions, such as temperature gradients or non-homogeneous input thickness profiles, may lead to a non-rectangular plate contour. A continuum mechanics approach is employed to systematically derive the contour evolution of the plate based on the input and output thickness. The mathematical model covering deviations in two dimensions is solved using methods for plane problems in mechanics. A comparison between the simulated contour evolution and measurement data from a real rolling process indicates the good accuracy of the model. Moreover, the model can be executed within one millisecond on a standard computer which stresses its real-time capability. A short analysis of the main reasons for the generation of camber utilizing the proposed model is presented.